Two robots moving geodesically on a tree

Donald M. Davis; Michael Harrison; David Recio-Mitter

doi:10.2140/agt.2022.22.785

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arXiv · 2006.14772

Two robots moving geodesically on a tree

Donald M. Davis·Michael Harrison·David Recio-Mitter

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Abstract

We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the $\ell_1$ and $\ell_2$ metrics. We determine the geodesic complexity of the ordered two-point $\varepsilon$-configuration space of any star graph in both the $\ell_1$ and $\ell_2$ metrics and of the unordered two-point configuration space of any tree in the $\ell_1$ metric, by finding explicit geodesics from any pair to any other pair, and arranging them into a minimal number of continuously-varying families. In each case the geodesic complexity matches the known value of the topological complexity.

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Donald M. Davis, Michael Harrison, David Recio-Mitter. 2020-06-26. Two robots moving geodesically on a tree. https://doi.org/10.2140/agt.2022.22.785

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